notochord and swimming motions in sturgeon. John H. Long, Jr. ...... Thanks to Fred Nijhout and John Mercer of the Morphometrics Laboratory of the Program in.
Environmental Biology of Fishes 44 : 199-211,1995 . ©1995 Kluwer Academic Publishers . Printed in the Netherlands.
Morphology, mechanics, and locomotion: the relation between the notochord and swimming motions in sturgeon John H. Long, Jr. Department of Biology, Vassar College, Poughkeepsie, NY 12601, U.S.A . Received 7 .7.1992
Accepted 9.1 .1995
Key words : Axial skeleton, Bending stiffness, Hydrostatic pressure, Ecomorphology, Acipenser transmontanus Synopsis To examine the relation between morphology and performance, notochordal morphology was correlated with notochordal mechanics and with steady swimming motions in white sturgeon, Acipenser transmontanus . In a still-water tank, motions of four sturgeon varied with changes in swimming speed and axial position along the body. For a 1 .34 m sturgeon, slow and fast swimming modes were distinguished, with speeds at the fast mode more than two times those at the slow mode without changes in tailbeat frequency. This increase in speed is correlated with an increase in the body's maximal midline curvature (m'), suggesting a role for curvaturerelated mechanical properties of the notochord . Maximal midline curvature also varied with axial position, and surprisingly was uncorrelated with axial changes in the notochord's cross-sectional shape - as measured by height, width, inner diameter, and lateral thickness of the sheaths . On the other hand, maximal midline curvature was negatively correlated with the axial changes in the notochord's angular stiffness (N m rad - ') and change in internal pressure (% change from baseline of 58 .6 kPa), both of which were measured during in vitro bending tests . In vivo curvature and in vitro angular stiffness were then used to estimate the bending moments (N m) in the notochord during swimming . In the precaudal notochord, the axial pattern of maximal stiffness moments was congruent with the pattern of maximal notochordal curvature in the precaudal region, but in the caudal notochord maximal angular stiffness was located craniad to maximal curvature . One interpretation of this pattern is that the precaudal notochord resists bending moments generated by the muscles and that the caudal notochord resists bending moments generated by hydrodynamic forces acting on the tail .
Introduction The relation between a fish's swimming performance and locomotor morphology has important ecological and evolutionary consequences . Capturing prey, escaping predators, foraging, schooling, and migrating are but a few of the behaviors whose performance can be affected by differences in the shape of a fin or the size of a bony vertebral column . Thus functional morphology determines, in part,
the nature of an animal's interaction with its environment, and this interactive process is often studied within the framework of the field of ecomorphology (Wainwright 1991) . A tenet central to studies in ecomorphology is that morphology limits the performance or capabilities of an individual and hence its patterns of resource use (Arnold 1983, Wainwright 1991) . This central tenet is predicated on a fundamental assumption : there is a direct causal link between mor-
200 phology and functional attributes such as mechani-
within a broad continuum : cruisers, accelerators,
cal properties. An operational framework built up-
and maneuverers . Cruisers are typified by tunas
on this fundamental assumption must be cautiously
(Scombridae), whose narrow caudal peduncle, lu-
implemented, since, as Burggren & Bemis (1990)
nate tail, and streamlined body provide maximal
document, the same function can be elicited from
forward thrust with minimal lateral motions . Accel-
different morphologies and, on the other hand, different functions can be elicited from similar mor-
erators are typified by pikes (Esocidae), whose
phologies . This paper documents a similar incongruity, one in which axial variation in notochordal
vide maximal turning and acceleration forces . Ma-
mechanical properties - but not morphology - is correlated with regionally variable swimming mo-
dontidae), whose discoid lateral profile and pre-
tions . The fundamental assumption that morphology
thrust and point-load braking forces . While inter-
and function are thightly linked can be treated as a
clear functional connection between body mor-
primary hypothesis of ecomorphology . Only if this
phology and swimming performance .
broad lateral profile and caudad median fins proneuverers are typified by butterflyfishes (Chaetodominant use of paired fins provide bi-directional mediate forms exist, these three categories draw a
hypothesis is supported, by either correlative or
On the other hand, given body shapes that are
causal evidence, can the second step, examining the
similar, how can differences in swimming speed be
relation between functional attributes and performance, be taken . If, in turn, evidence is found to
explained? Scup, Stenotomus chrysops, can swim
support a causal link between functional attributes
ing only red, aerobic muscle (Rome et al . 1992) . In
and performance, the originally assumed connec-
spite of higher tailbeat frequency in scup, faster
tion between morphology and performance is supported . With this explicitly plausible foundation,
speed is not caused by a faster velocity of muscle
the investigator may proceed, with the likelihood increased of finding meaningful results, to examine
scup swim faster by using a `less undulatory' style of
the ecological consequences of morphological vari-
that of carp.
ation .
twice as fast as common carp, Cyprinus carpio, us-
contraction . Instead, Rome et al. (1992) suggest that swimming : the curvature of the body is less than Since curvature is the result of the bending of the
With these prerequisites in mind, this study seeks
body, any morphology constraining bending would
to provide, by example, a methodology for the test-
influence curvature and hence have a direct effect
ing of the relation between morphology and performance . In order to examine how the axial skele-
on swimming speed . One likely morphological fac-
ton of fishes, its functional attributes, and swim-
sections where much of the area is located laterally
ming performance are related, I have two general goals : (1) to test the hypothesis, using correlative
and distally from the axial skeleton will have
and biomechanical techniques, that the gross mor-
where much of the area is located dorso-ventrally or
phology of the white sturgeon's notochord is relat-
is reduced altogether (Wainwright et al . 1976) . An-
tor is the cross-sectional shape of the body . Cross-
greater resistance to lateral bending than those
ed to its mechanical properties and (2) to relate the
other likely morphological factor is the number of
notochord's mechanical properties to the swim-
vertebral segments (for review see Lindsey 1978) .
ming performance of an individual sturgeon.
Fishes with many vertebrae, such as eels, tend to bend their bodies more sinuously during swimming
Locomotor morphology and performance
than fishes with fewer vertebrae, such as scombrids . This correlation raises the following question : the number of segments might affect with functional at-
The aspect of fish morphology that has received the
tribute of the axial skeleton bends and that would,
most attention as a determinant of swimming per-
in turn, limit the amount of bending? The intervertebral joints in blue marlin, Makaira nigricans, have
formance is external body shape . Webb (1984) delineated swimmers into three specialized categories
substantial and regionally variable bending stiff-
2 01 ness (Long 1 .992) . Hence bending stiffness may limit
Methods
swimming motions: it determines the amount of bending moment - the product of force and a'lever' arm - needed to bend the intervertebral joints and
Study animals
hence the entire axial skeleton .
Five white sturgeon, Acipenser transmontanus, all females 5 to 6 years old, were studied. They were raised from eggs and kept in circular tanks, 4 m in
The notochord and swimming motions
diameter. Overall body weights at the time of this study were 10 .4, 11.3, 14 .4, 17 .3, and 20 .4 kg . The
The axial skeletons of fishes vary in structure from
overall lengths, from the tip of the rostrum to the
unconstricted notochords to fully ossified vertebral
end of the caudal fin, were, in an order correspond-
columns . Adult Acipenseriformes, the sturgeons
ing to the weights above, 1 .20, 1 .25, 1 .34, 1.43, and
and paddlefishes, are one of the few groups to retain
1 .32 m .
a notochord, which lacks intervertebral joints while possessing a. continuous internal lumen filled with vacuolated cells (Goodrich 1930) . This persistent
Kinematics of swimming
notochord is correlated with swimming motions that differ from those of vertebrated species . Lake
The swimming motions were video-taped in a 3 m
sturgeon, A cipenserfulvescens, modulate three kin-
by 10 m still-water tank as fish swam over a 2 m by
ematic variables with increasing speed : tailbeat fre-
3 m grid of 10 cm squares, which was located in the
quency, tailbeat amplitude, and propulsive wave-
middle of the tank to allow room at either end for
length, which is the length of the body's undulatory
turns and acceleration to cruising speeds . A 1.2 m
wave as it appears from superimposed midline im-
by 1 .8 m mirror was mounted over the tank at 45°
ages of one tailbeat cycle (Webb 1986) . On the other
angle with respect to the grid, reflecting the dorsal
hand, many teleost species modulate only one or
view of the swimming sturgeon to a Magnavox
two variables: tailbeat frequency and sometimes
SVHS Video Escort model VR9206AV01 Camcor-
tailbeat amplitude (Bainbridge 1958, Webb et al .
der mounted 5 m away.
1984) . Thus, because of their notochordal structure
Only the 1 .34 m sturgeon swam over a wide range
and complex swimming kinematics, sturgeon are
of speeds . Three others (1 .20 m, 1.25 m, and 1 .32 m)
ideal for the study of the relation between axial
swam slowly and provided supplementary data on
morphology and swimming motion .
swimming kinematics ; they could not be provoked
The following specific questions are addressed in
to swim faster . The 1 .43 m sturgeon never swam in a
this study: (1) How do the kinematics of swimming
manner that could be analyzed. As a result, the ana-
change with increasing speed in sturgeon? (2) How
lyses and conclusions drawn in this paper are based
does the morphology of the notochord vary region-
on kinematic and mechanical information taken
ally and is it correlated with curvature during swim-
primarily from the 1 .34 m sturgeon, and generaliza-
ming? (3) How do the bending mechanics of the no-
tions should be interpreted cautiously . I was able to
tochord vary regionally and are they correlated
record the 1.34 m sturgeon swimming at higher
with curvature during swimming? (4) Is the swim-
speeds because I discovered, quite by accident, that
ming speed of sturgeon constrained by the noto-
sturgeon swim faster at night . Because of the high
chord?
light sensitivity of the video camera, I was able to film the sturgeon before sunrise and capture its fast swimming . All swimming sequences were filmed at a shutter speed of 1 ms . The criteria for choosing any swimming sequence for analysis were as follows . The sturgeon must swim in a nearly straight line at a constant velocity
2 02 while on camera, a time which varied from no fewer
late the distance from point to point, which yielded
than 4 to no greater than 6 complete tailbeats . Stea-
the axial position corresponding to each value of x.
dy swimming in the 1 .34 m sturgeon readily met
The accuracy of this method of measuring curva-
these requirements, since this individual cruised
ture is a mean of 95% ±2.1% (1 S.D.) and was esti-
continuously around the tank . The sequences were
mated as follows . A rope of 20 cm length was
analyzed using a video-digitizing system developed
wound around one side of the circumferences of
by Crenshaw (1992) . Using a Sony B VU-920 Video-
three disks of increasing radius arranged side by
cassette Player and a Commodore Amiga A2000
side . In this manner, the rope approximated the
Microcomputer, video fields were overlaid onto a
midline curvature of a fish during steady swimming .
computer-generated cursor field via a video gen-
The maximal curvature of the rope was limited
lock device. The manually-controlled cursor re-
along its length by the radius of each disk . Thus the
corded x and y coordinates along the dorsal midline,
maximum possible curvature was known a priori at
which is commonly used in locomotor studies to represent the overall motion of the fish (Yates 1983,
three places along the rope . The rope and disks
Hess & Videler 1984, Videler 1985, Van Leewen et al . 1990) . This midline is assumed, without evidence,
digitized .
were then videotaped in the experimental tank and
to be the position of the axial skeleton (however, Van Leewen et al . 1990 cite unpublished x-ray cine-
Morphology of the notochord and correlated
matographic data of free-swimming carp to support this claim) . To represent the position of the midline
mechanics and curvature
through time, 35 points were taken every tenth of a
At the same axial positions where mechanical tests
tailbeat cycle .
were made and curvature was calculated, gross as-
Midline curvature at any time was calculated as a
pects of notochordal structure were measured . The
function of axial position . Curvature, K in m- ', is the inverse of the radius of curvature at any point on a
following cross-sectional measurements were cho-
smooth line (Gillet 1984) . Using the digitized points
mine the second moment of area, which is propor-
for the midline, a curve was fit in the form of a poly-
tional to flexural stiffness (Wainwright et al. 1976) :
sen because in man-made structures they deter-
nomial equation using the SYSTAT statistical pack-
(1) diameter of the pressurized core, (2) transverse
age (Wilkinson 1989) . This regression line, which
radial thickness of the notochordal sheaths, (3)
could be a third- to fifth-order polynomial, was plotted with the data points to visually verify accu-
width of the notochord, and (4) overall transverse height of the notochord .
racy. With a good visual and high statistical fit (R 2 > 0.98), the polynomial was then used to derive an
These measurements were used as independent
equation for curvature as a function of x. If the fit of
variables in a step-wise linear regression analysis (Wilkinson 1989) to determine their ability to pre-
the regression did not meet these criteria, the data
dict the angular stiffness (see next section) at each
set was subdivided and an equation was fit to those subsets . The equation for curvature is as follows
position . An identical analysis was run using curvature of the notochord as the dependent variable .
(Gillet 1984) : K=
y"I (1) (1 + y,
Mechanical properties of the notochord
where y' is the first derivative and y" is the second
Following death, notochords were dissected out of
derivative of the polynomial regression . To Plot K as a function of axial position, each x coordinate from
the sturgeon and kept intact, including the head and tail, so as to preserve the integrity of the pressurized
the midline points was first used to calculate K at
internal core. Notochordal pressure was monitored
that point . Then, beginning with the first midline point, the Pythagorean theorem was used to calcu-
from the beginning of the dissection to the end of the mechanical tests (see below) . No significant
203 changes in baseline pressure were found during this period, which could last up to 6 hours. During that time, the notochord was continually bathed in physiological saline (Randall & Hoar 1971).Because of technical difficulties, pressure was not measured in the 1.43 m sturgeon. Seven 1 cm long sections of the intact notochord were separately forced to bend sinusoidally at amplitudes off 3.3” and f 5.0” using a dynamic bending machine (Long 1992). This machine measures the bending moment needed to cause the sinusoidal motion of the notochordal section. Given the bending moment, M, and a sinusoidal bending motion, sin(wt), a solution to the differential equation of motion for a single-degree-of-freedom system can be found (Den Hartog 1956): M,(sin(wt) = kQin(w-8) + cO,w cos(wt-8) It!l,w2sin(wt-S), (2)
3.3” was 11.5m-’ and 17.5 m-’ for 5.0”. These curvatures are an order of magnitude higher than the maximal midline curvatures measured during swimming (see Results); they are the smallest curvatures possible given the resolution of the bending apparatus. Using in vitro angular stiffness and in vivo curvature data from the 1.34 m sturgeon, the maximal in vivo stiffness moment was estimated at the seven test positions on the notochord. The maximum in vivo curvature of a section of the notochord was multiplied by a conversion factor of 0.0058568 rad m, which is the ratio of the bending amplitude of 0.0873 radians (5.0”) and the average bending test curvature, K, of 14.9 m-’ (see previous paragraph). This gave the in vivo curvature in radians, which was then multiplied by the angular stiffness to calculate the maximum stiffness moment occurring at that point in the notochord (see first term on righthand side of Equation 2).
which can also be stated in words as: bending moment = moment due to stiffness + moment due to damping - change in angular momentum, where M, is the amplitude of the sinusoidal bending moment (N m), w is the angular frequency (s-l), t is time (s), k is the angular stiffness (N m radian-‘), 8, is the amplitude of the sinusoidal bending displacement (radians), 6 is the phase lag (radians), between the displacement and the bending moment, c is the damping coefficient (kg m2 rad-* s-‘), and I is the moment of inertia (in kg m2 rade3). Notochordal curvatures generated during these bending tests were calculated as follows. Each 1 cm section of notochord was assumed to bend laterally about a uniaxial hinge located in the middle of the section. Depending on the testing amplitude, the angular displacement of the hinge was either 3.3”or 5.0”. To calculate curvature, K, its inverse, the radius of curvature, was computed as the radius of the arclength of a central angle in radians. From geometry, the central angle was either 3.3” (0.0576 radians) or 5.0” (0.0873 radians) and the arclength was the length (m) of one-half of the test section in m. When the test section wasO.O1m long, curvature for
Pressure within the notochord
Pressure in the cavity of the notochord, which contains large vacuolated cells, was measured using an Entran Devices EPB-125U-25SY pressure transducer (5 0.25% linearity to 172 kPa; sensitivity of 0.27 mV kPa-‘). The transducer, which was 3 mm in diameter, was sealed in a 10 cc syringe, leaving only a hole for the needle. To this hole a 16 gauge needle filled with vegetable oil, used to prevent the formation of air bubbles, was attached after filling the syringeal reservoir with oil as well. The needle was then inserted through the notochordal sheaths and into the vacuolated core no later than 15 minutes after the sturgeon had been killed. The transducer remained in the core during dissection and all subsequent mechanical tests. A voltage proportional to the internal pressure was developed using a Gould 13 161330DC Bridge Preamplifier.
Results There was a discontinuity in the swimming speeds of the 1.34 m sturgeon, where for tailbeat frequen-
204
17
e v a N OI
b
E 3N 0.2
0 .4
0.6
10 cm 0 .8
1 .0
1,2
1 .4
Tailbeat frequency (Hz) Fig. 1. Swimming speed of white sturgeon as a function of tailbeat
C
frequency. Swimming speed is given in body lengths per second for the four sturgeon ranging in size from 1 .25 m to 1 .43 m. Using the eight data points from the 1 .34 m sturgeon in the slow mode, the bottom line is described by a regression equation (R 2 = 0 .741 ; p = 0.006) : y = 0 .005 + 0.138 x, where y is the swimming speed (I s') and x is tailbeat frequency (Hz) . No significant non-zero
10 cm
slope was detected for the 1 .34 m sturgeon in the fast mode .
cies between 0 .7 and 0 .83 Hz the swimming speeds differed more than two-fold (Fig . 1) . Only the
Fig. 2 . Motions of the notochord during slow and fast swimming modes: a - A dorsal view of the 1 .34 m sturgeon swimming over the kinematic grid. b - Ten successive positions of the notochord
1 .34 m sturgeon swam in the two modes, and the da-
during a complete slow-mode tailbeat, at a tailbeat frequency of
ta from the 1 .25 m, 1 .32 m, and 1 .43 m sturgeon are included to show that for the slow mode the relation
0 .64 Hz and a swimming speed of 0 .10 m
between swimming speed and tailbeat frequency is similar for all individuals . The kinematics of the notochord during the two different modes is illustrat-
s ' or
0 .07 body lengths
s-' . c - Ten successive positions of the notochord during a complete fast-mode tailbeat, at a tailbeat frequency of 1 .00 Hz and a swimming speed of 0 .35 m s:- 'or 0 .27 body lengths s -' . The arrows are vectors whose magnitude and orientation represent the speed and direction of movement .
ed in Figure 2 . In the fast mode, the magnitude of curvature along the midline increased (Fig . 3) . In the 1 .34 m sturgeon, cross-sectional height,
plitude of 3 .3° . Note that the angular stiffness decreased with increasing frequency.
width, inner core diameter, and radial sheath thick-
The baseline pressure of the notochord, taken
ness all decreased from head to tail (Fig . 4) . In a
when the body was straight, was 58 .6 kPa above am-
step-wise linear regression, no subset of the morph-
bient in the 1 .34 m sturgeon . For the four sturgeon
ological characters was significantly correlated with
measured, the mean notochordal pressure was
either in vitro angular stiffness, k, at an amplitude of
60.8 kPa above ambient . This baseline pressure fluctuated during the in vitro bending tests . In the
5° and frequencies of 0 .5 and 1.0 Hz, or in vivo maximal curvature, x.
1 .34 m sturgeon, the greatest change in pressure,
Angular stiffness, k, of the notochord varied with
Op, occurred during the bending of the notochord
position and bending frequency at a bending amplitude of 5 .0° in the 1 .34 m sturgeon (Fig. 5) . Maximal
just anterior to the position of the pelvic fins (Fig.
angular stiffness occurred just anterior to the pelvic fins, which were located at 52% of the overall length. The pattern was the same at a bending am-
5) . The change in pressure, Ap, was correlated with the angular stiffness, k, at bending amplitudes of 3 .3° and 5 .0° (Fig . 5) . Angular stiffness, in turn, was significantly correlated with the maximal in vivo
20 5 curvature during the slow swimming mode (Fig . 5) .
that involves the restriction of lateral bending and
Maximal curvature, x, during both slow and fast
muscle antagonism .
modes, was correlated with change in pressure, Op, which is independent of frequency (Fig . 5) . The maximal in vitro stiffness moments along the notochord, at a bending amplitude of 5 .0°, are
Swimming motions
greatest near the pelvic fins (Fig . 6) . In comparison, the in vitro damping moments, calculated using the
The range of swimming speeds - from 0 .1 to 0.25 1 s -'
second term on the right-hand side of equation 2,
an order of magnitude slower than that in 10 cm
are included to show that at physiological tailbeat frequencies their effect is relatively small . The pat-
long lake sturgeon, although the absolute speeds of
tern of in vivo stiffness moments is quite different
slow speeds in this study may be the result of several
than that of the in vitro stiffness moments (Fig . 6) .
factors . First, the sturgeon were not examined in a
During both slow and fast modes, the maximal in
flow tank where swimming speed can be controlled .
vivo stiffness moments occur just posterior to the
This should not have been a significant factor, how-
pelvic fins ; thus, the axial pattern of in vivo stiffness moments in the notochord differs from the axial
ever, since Webb (1986) found that lake sturgeon
pattern of in vitro angular stiffness (Fig . 5) while
tanks . Second, the white sturgeon were an order of
corresponding to the axial pattern of in vivo curva-
magnitude larger than the lake sturgeon . Dividing
ture (Fig . 3) .
absolute swimming speed by body length usually
(Fig . 1) - for the four white sturgeon examined were
0 .10 to 0 .40 m s- ' were similar (Webb 1986) . The
behaved similarly in both flow tanks and still-water
adjusts for size differences, placing individuals of the same species but of different size on the same Discussion
line of tailbeat frequency versus non-dimensionalized swimming speed (Bainbridge 1958) . When this
The results of this study must be viewed with cau-
comparison is made between white and lake stur-
tion because most of the data comes from only one
geon, the line is discontinuous, suggesting a species-
sturgeon. For reasons unknown - no morphological
specific difference . Third, the white sturgeon used
differences in external or internal structure were
in this study were reared in captivity, and, as a re-
detected - three of the four experimental animals swam only at very slow speeds (Fig . 1) . The one that
sult, their activity metabolism may have been af-
swam at faster speeds displayed curvature-modu-
fected . The axial pattern of maximal notochordal curva-
lated swimming motions, which were used to probe
ture of the 1 .34 m white sturgeon (Fig . 3) is unusual
the functional relation between motion and the me-
compared to that in teleosts. Moving caudally in the
chanics and morphology of the notochord .
sturgeon, the maximal midline curvature decreases
No support was found for the hypothesis that no-
near the pelvic fins and increases again towards the
tochordal morphology is closely tied to its functional attributes. Rather the functional attributes of the
tail ; this pattern was also seen in the other sturgeon filmed in this study . Within teleosts, the maximum
notochord - its mechanical properties - appear to
curvature during steady swimming increases mo-
be more closely related to swimming motions, for
notonically from head to tail (Hess & Videler 1984,
angular stiffness and change in baseline pressure
Webb 1988) . Thus in our 1 .34 m sturgeon, the propa-
correlate negatively with the curvature of the body
gation of the undulatory wave is not simple, and, if
during swimming. The incongruity between notochordal morphology and swimming motions under-
this pattern persists in other species of sturgeon, it suggests that the undulatory mechanisms of stur-
scores the importance of testing this relation as a
geon are different from those of teleosts .
prerequisite for any ecomorphological study . Final-
In addition, axial curvature is modulated, in a
ly, using mechanical and kinematic information, a
way never described in fishes, to permit the 1 .34 m
locomotor function is posited for the notochord
sturgeon to change from one undulatory `mode' to
206
a
0%
19
52
61 86
77
100%
b E
2 .0
1 .5
b • •
1 .0
Y
• 0
10
20
30
40
50
60
70
80
90
100
Axial position (% of overall length)
Fig. 3 . The maximal in vivo curvature of the notochord during slow and fast mode swimming in the 1 .34 m sturgeon : a - Dorsal and lateral views of the sturgeon to show the relative positions of
0
10
20
30
40
50
60
70
80
90
100
Axial position (% of overall length)
fins . b - Maximal in vivo curvature of the notochord at the seven different axial positions at which bending experiments were con-
Fig . 4. Cross-sectional morphology of the notochord in relation
ducted . The numbers by each datum indicate the relative timing of the curvatures during the tailbeat . These data were calculated
to axial position in the 1 .34 m sturgeon: a - Diagrammatic cross-
from the midlines in Figure 2.
section of notochord showing the measurements taken at each of the seven positions at which bending experiments were conduct-
another (Fig. 1) . During the slow mode, swimming
functions of axial position . For cross-sectional height (cm), the
ed. b - Variation in the four cross-sectional morphologies as
speed of this individual could be predicted from the
following regression equation was found (n = 7 ; R Z = 0.757 ; p =
tailbeat frequency alone. However, should this stur-
0 .011) : y = 7 .38 - 0.044 x, where y is the height and x is the axial position. For cross-sectional width (cm), the following regression
geon choose to swim at the fast-mode speeds, a tail-
equation was found (n = 7 ; RZ = 0 .848 ; p = 0 .003) : y = 4 .92 - 0.045
beat frequency of 0 .8 Hz could be held constant
x, where y is the width and x is the axial position . For cross-sec-
while the curvature of the body increased, generat-
tional diameter (cm), the following regression equation was found (n = 7 ; RZ = 0.683; p = 0 .022) : y =1 .67 - 0 .007 x, where y is
ing greater than a twofold increase in swimming
the diameter and x is the axial position . For cross-sectional thick-
speed (Fig. 3) . While in the 1 .34 m sturgeon the two swimming
ness (cm), the following regression equation was found (n = 7 ; RZ = 0.764; p = 0.010) : y = 1 .63 - 0 .019 x, where y is the thickness
modes appear to be discontinuous on the plot of
and x is the axial position .
swimming speed and tailbeat frequency (Fig . 1), the following question arises : can the sturgeon continuously vary curvature to achieve intermediate speeds? As mentioned in Methods, the sturgeon
207
a
16
2.4
b
2.49 dkad0 .5Hz 0kst1 .0Hz Lop a10.5 Hz &1 .0Hz
a u
1 .8 `o
1 .2 )
d CL. c 0.6
a
C
ai 0 _, 0.0 u 0 10 20 30 40 50 60 70 80 90 100 a. a Axial position (% of overall length) j
a1 0
h
0 0 .1 0 .2 0.3 0.4 0 .5 0.6 0 .7 p, change In pressure (% of baseline)
A
d
C
2 .0
2.0 .
N
.
.
E O slow • fast
0
U X
0 0
1 .2 1 .8 0.6 k, angular stiffness (N m red
2.4
_1
)
0
0
o p,
0 .1 0 .2 0.3 0 .4 0 .5 0.6 0 .7 change In pressure (% of baseline)
Fig. 5. The mechanical properties of the notochord of the 1 .34 m sturgeon in relation to axial position and in vivo curvature : a - Angular
stiffness at a bending frequency of 0 .5 and 1 .0 Hz and a bending amplitude of 5 .0°, as a function of axial position. Change in the baseline pressure of the notochord during bends of amplitude 5 .0° at 0 .5 and 1 .0 Hz as a function of axial position . b - The relation between the angular stiffness and the change in notochordal baseline pressure . For angular stiffness, k, at a bending frequency of 0 .5 Hz the following regression equation is given (n = 7 ; R2 = 0.592 ; p = 0 .043) : y = 0 .60 + 2.11 x, where y is angular stiffness and x is change in pressure (% of baseline) . For angular stiffness, k, at a bending frequency of 1 .0 Hz the following regression equation is given (n = 7 ; R2 = 0.655 ; p = 0 .027) : y = 0 .53 + 1.54 x, where y is angular stiffness and x is change in pressure. c - The relation between the in vivo maximal curvature and the angular stiffness of the notochord. For maximal curvature, K, during the slow mode (tailbeat frequency of 0 .64 Hz) as a function of angular stiffness, k, at a bending frequency of 0 .5 Hz, the following regression equation is given (n = 7 ; RZ = 0 .752 ; p = 0 .011) : y = 1.84 - 0.67 x, where y is the maximal curvature and x is the angular stiffness . For maximal curvature, x, during the fast model (tailbeat frequency of 1 .0 Hz), as a function of angular stiffness, k, at a bending frequency of 1 .0 Hz, no significant non-zero slope could be detected . d = The relation between the in vivo maximal curvature and the change in baseline pressure . For maximal curvature, x, during the slow mode the following regression equation is given (n = 7 ; R2 = 0 .845 ; p = 0.003) : y = 1 .67 -1 .99 x, where y is the maximal curvature and x is the change in pressure . For maximal curvature, x, during the fast mode the following regression equation is given (n = 7 ; R' = 0 .803 ; p = 0 .006) : y = 2 .24 - 2 .01 x, where y is the maximal curvature and x is the change in pressure .
208 swam freely in a still-water tank . Only with changes in light intensity did the 1 .34 m sturgeon change speed . Over one morning, the 1 .34 m sturgeon was videotaped continuously as the sun rose and its swimming speed decreased . At no time did the sturgeon exhibit intermediate speeds for a constant tailbeat frequency - it was as though the individual `switched gears' from high to low curvature . This discontinuity does not mean that the sturgeon was incapable of continuous modulation of curvature, only that it was not observed . It also remains to be shown if sturgeon in general exhibit this pattern and if sturgeon swimming in flow tanks can be induced to change modes. It should be noted that the 1 .34 m sturgeon was morphologically similar to the other individuals in external and notochordal morphology.
0 .8 Hz ∎ stiffness moment 0 damping moment 1 .0 Hz D stiffness moment B damping moment
30 .6
38 .1
45.5
53.0 59.7
66 .4
73 .1
Axial position (% of overall length)
b
0.014
fast mode
slow mode
Morphology of the notochord is not correlated with curvature or functional attributes
Four characteristics of the cross-sectional morphology of the notochord all decrease significantly from head to tail in the 1.34 m white sturgeon (Fig . 4) . This pattern, however, does not correspond to the pattern of notochordal curvature measured during swimming (Fig . 3) . This lack of a correlation is curious, since the cross-sectional characteristics were chosen because they should theoretically be proportional to flexural stiffness of the notochord via the second moment of area, I (Wainwright et al . 1976) : I = 0.25 n (R 4 - r4), where R is the outer radius and r the inner radius of the notochord. For homogenous structures, the flexural stiffness is the product of the second moment of area and the bending modulus of the structure, which is its linear ratio of stress to strain . It is possible that as I decreases along the notochord with decreasing cross-sectional dimensions, the modulus of the structure, which is dependent on its material properties, could be increasing independently. It is clear that the notochord is not a simple beam .
H neurocranium
pelvic fins
caudal fin
0.000 0
10
20
30
40
50
60
70
80
90
100
Axial position (% of overall length)
Fig. 6. Maximal bending moments generated by the notochord in resistance to bending : a - Bending moments due to the stiffness and damping properties of the notochord for each 1 cm section of notochord bent at an amplitude of± 5 .0° . Damping moments are included to illustrate their relative unimportance . b - The in vivo stiffness moments in the notochord during the slow and fast modes in Figure 2 . See Methods for calculations .
This statement receives further support from the fact that the morphological characteristics of the notochord were also uncorrelated with the functional attributes of the notochord, angular stiffness and change in notochordal pressure . Thus, no evidence was found to support the ecomorphological hypothesis that morphology and function are tightly linked. The data presented, however, are correlative, and thus should not be viewed as a decisive refutation of this hypothesis . Nonetheless, no basis exists for an ecomorphological study of the notochord and swimming performance . The lack of a correlation may be due, in part, to the hydrostatic pressure of the notochord and its
20 9 changes during bending, which complicate a simple
bending stiffness is related to the in vivo notochor-
beam-theory explanation of the relation between
dal curvature in ways that suggest it may play a role
the local mechanical properties and local morphol-
in determining the regional locomotor functions of
ogy. The internal notochordal pressure in the 1 .34 m
the notochord .
sturgeon was 58 .6 kPa above ambient, which is
Axial curvature is a key kinematic variable con-
large enough to pre-stress the notochordal sheaths - if the notochord behaves like a pressurized, thinwalled cylinder (Den Hartog 1949) - just as the
trolling swimming speed . Rome et al . (1992) have demonstrated in scup, Stenotomus chrysops, and carp, Cyprinus carpio, that when only the red mus-
swelling pressure of water increases resistance to
cle is used during undulatory swimming, the differ-
compression by pre-stressing the tensile fibers in
ence in swimming speeds in the two species is a
the intervertebral disks of humans (Vincent 1990) . inherent in the material of a structure in the absence
function of the undulatory curvature, and not muscle physiology . When scup are swimming twice as fast as carp, the maximal velocities of muscle short-
of external loads (Faupel 1964) . With external
ening in the two species are virtually identical, but
loads, such as those applied when bending a small
the curvature of the body is much less in the faster
section of the notochord, increases in internal pres-
scup. Little axial curvature results in a smaller ex-
sure were generated and then transmitted through the lumen to all parts of the notochord . Thus by
cursion of the sarcomeres, which is compensated for by a higher tailbeat frequency . This reduction of
transmitting and diffusing the forces of localized
curvature in the scup may decrease drag, thus al-
bending, hydrostatic pressure behavior may obfus-
lowing for high swimming speeds while maintaining
cate the local relations between morphology and
the same maximal velocities of muscle shortening
angular stiffness .
as the carp.
Pre-stress, also known as initial stress, is the stress
For the 1 .34 m white sturgeon, the presumed benefit of increased axial curvature with swimming Stiffness and change in pressure are correlated with
speed (Fig . 3) is that the excursion of the sarco-
axial curvature
meres, and hence muscle shortening velocity, can be increased . Thus when tailbeat frequency is held
In contrast to notochordal morphology, the func-
constant in both slow and fast modes, the maximal
tional attributes, angular stiffness and change in
muscle velocity will be higher with greater curva-
pressure, were negatively correlated with maximal
ture, resulting in faster speed by way of increased
curvature of the notochord during slow and fast modes (Fig. 5) . It remains for experimental studies
power output (where power is the product of force
to demonstrate a causal link between stiffness of the
muscle shortening velocity to the maximal shorten-
notochord and curvature during swimming, since
ing velocity remains within a range of 0 .17 to 0 .36,
other factors, such as body shape and muscle activ-
where maximal power is produced (Rome et al .
ity, could follow the same axial pattern as the angular stiffness . Nonetheless, given this correlation, it is
1992) . Hydrodynamically, however, there should be
mechanically reasonable to predict a causal rela-
resulting power output cannot compensate for the
tion.
added drag incurred by the increasing curvature of
and velocity) . This is provided that the ratio of the
a point at which the increased muscle velocity and
the body. It is possible that limits on the curvature of the Is swimming speed limited by the notochord?
body are caused, in part, by the notochord . The evi-
Without examining the mechanics of muscle, skin,
dence presented here shows that the curvature of the body is inversely proportional to the angular
and body shape, it cannot be said with certainty to
stiffness and change in baseline pressure of the no-
what degree the notochord limits the swimming speed of white sturgeon . However, the notochord's
butes increase with a change in position (Fig. 5), the
tochord (Fig . 5) . As both of these functional attri-
210 in vivo maximal curvature at a given axial position
Acknowledgements
decreases (Fig . 5) . The critical mechanical factor, however, is not the stiffness or change in pressure
This study would not have been possible without
per se, but the resistance they give the notochord to
Sergei Doroshov of the Department of Animal Sci-
external bending moments . By knowing the angular
ence at the University of California at Davis, who
stiffness and in vivo curvature at a position on the notochord, the in vivo stiffness moments can be cal-
provided white sturgeon, generous assistance, and
culated (Fig . 6) . During both slow and fast modes, it
ry, especially Chris Alexander for her outstanding
appears that local bending moments in the precau-
logistical assistance and troubleshooting . Paul Lutz,
dal region, presumably generated by the lateral
the Director of the Institute of Ecology and UC Da-
myotomal muscles, are responsible for the local
vis, graciously provided his time and research facilities . Thanks to Fred Nijhout and John Mercer of
curvature of the body, as indicated by the correlation of in vivo stiffness moments and in vivo curva-
advice . Thanks also to the members of his laborato-
ture. Starting at the pelvic fins, however, the rela-
the Morphometrics Laboratory of the Program in Biological Structure at Duke University and Hugh
tion between maximal bending moments and cur-
Crenshaw for assistance with the motion analysis .
vature changes, with the maximal stiffness mo-
During the experimental portion of this work, I was
ments of the notochord occurring anterior to
funded by a Cocos Fellowship in Morphology from
maximal curvature . This relation suggests different regional functions for the notochord : (1) the pre-
the Cocos Foundation of Indianapolis, Indiana . A portion of the analytical section was funded
caudal section of the notochord acts as a resistor to
by a grant from the Office of Naval Research
bending, limiting curvature and acting as a muscle
(# N00014-93-1-0594) . The organizers of the Eco-
antagonist, and (2) the caudal section of the noto-
morphology of Fishes symposium, Phil Motta,
chord acts like a cantilevered beam anchored at the
Steve Norton, and Joe Luczkovich, and the editor of
pelvic fins, resisting bending moments generated by
this volume, Karel Liem, deserve thanks for their
the movement of the free end of the tail through the
organization and editorial assistance. Two anony-
water. This hypothesis does not exclude other func-
mous reviewers provided constructive comments .
tions, such as elastic energy storage, which could be
Special thanks go to Steve Wainwright, who provid-
acting during recoil .
ed the intellectual environment in which to pursue
As a resistor of externally applied bending mo-
this work .
ments, the notochord may limit swimming speed by placing an upper limit on the bending moments that can be generated by the musculature . For example,
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